Image copyrightReutersImage caption
The US and South Korea hold regular joint live-fire exercises

The Kim-Trump summit - the first such meeting between the two countries - centred on nuclear disarmament and reducing regional tensions. It concluded with a one-page agreement.

In the press conference afterwards, however, Mr Trump added another announcement: the cancellation of the military exercises.

The drills, often called "war games", are held in South Korea with local forces and US soldiers stationed there.

Image copyrightReuters

Mr Trump also said he wanted to bring US troops home - although he did not specify a timeframe.

He said the drills were "provocative" - even though the US has previously defended them - and there were suggestions that US allies had not been forewarned of this move.

South Korea's Presidential Blue House said it needed "to find out the precise meaning or intentions" of Mr Trump's statement.

South Korean President Moon Jae-in spoke by phone with Mr Trump for 20 minutes late on Tuesday, but an official readout of the call made no mention of military exercises, according to Reuters.

Did the Pentagon know?

The previous day US Defence Secretary Jim Mattis told reporters he did not believe that troop levels were on the agenda. When asked if he would know if such discussions were planned, he said, "Yeah, I sure would."

Image copyrightGetty ImagesImage caption
There are thousands of US soldiers in South Korea

However, the Pentagon has since denied that Mr Mattis was caught off guard. He was consulted ahead of time, said Pentagon spokesperson Dana White.

In a statement sent to the BBC, she said: "Our alliances remain ironclad, and ensure peace and stability in the region."

What else has Donald Trump said?

In a flurry of tweets later on Tuesday, Mr Trump said there was "no limit" to what North Korea could achieve if it gave up its nuclear weapons.

He thanked Mr Kim for "taking the first bold step toward a bright new future for his people" and said the world had taken "a big step back from potential nuclear catastrophe".

The World has taken a big step back from potential Nuclear catastrophe! No more rocket launches, nuclear testing or research! The hostages are back home with their families. Thank you to Chairman Kim, our day together was historic!

Heading back home from Singapore after a truly amazing visit. Great progress was made on the denuclearization of North Korea. Hostages are back home, will be getting the remains of our great heroes back to their families, no missiles shot, no research happening, sites closing...

The US president said he had, and repeated his description of Mr Kim as "talented".

Politics turned upside down

Analysis by Anthony Zurcher, BBC North America reporter

Two years ago Barack Obama travelled to Cuba - and was roundly denounced by conservatives for breaking bread with totalitarian leaders and praised by liberals for his statesmanship. Now, with Donald Trump's summit with Kim Jong-un, the tables have been turned. Mostly.

On conservative Fox News and among Mr Trump's core supporters, the president was lauded for a historic diplomatic breakthrough. Among Democrats, there was more than a fair amount of concern that the president was engaging in a glorified publicity stunt with little chance of success.

Republicans in Congress have been more measured. There was plenty of talk of "historic first steps", in Senate Majority Leader Mitch McConnell's words, but concern over how the yet-to-be negotiated verification details will turn out.

A few other conservatives expressed dismay at seeing the US and North Korean flags side-by-side, and viewed Mr Trump's solicitous manner and warm words for Mr Kim as too much, given his nation's history of human rights violations.